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1. Insert Presentation Title 1 September 2, 2012
2. Tale of Two Stocks (March 2012, #s are approx) Insert Presentation Title 2 September 2, 2012
3. Annual Price Chart: MSFT Insert Presentation Title 3 September 2, 2012
4. Annual Price Chart: GOOG Insert Presentation Title 4 September 2, 2012
5. Annual Chart Comparison Very hard to tell the difference between the two firms optically
Essentially, prices behave similarly on a macro scale Insert Presentation Title 5 September 2, 2012
6. MSFT: 5 minutes Insert Presentation Title 6 September 2, 2012
7. GOOG: 5 minutes Insert Presentation Title 7 September 2, 2012
8. Five minute chart comparison Visually, one can immediately distinguish GOOG from MSFT
Quote differences
MSFT quotes are stable for long periods of time
MSFT quotes move in discrete jumps
GOOG quotes move more continuously
Trade differences
MSFT trades much more frequently (and since average daily dollar trade volume is similar, trade sizes must be smaller)
Many MSFT trades occur within the spread, frequently at the mid-quote
GOOG trades less frequently, usually at one side of the spread
Q: What drives these differences?
A: Market microstructure
Minimum price variant is nominally $0.01 in both cases, which economically is 20x larger for MSFT than GOOG
Insert Presentation Title 8 September 2, 2012
9. What is Market Microstructure? Market microstructure is a branch of finance concerned with the details of how exchange occurs in markets. […] The major thrust of market microstructure research examines the ways in which the working processes of a market affects determinants of transaction costs, prices, quotes, volume, and trading behavior. [Source: Wikipedia]
Insert Presentation Title 9 September 2, 2012
10. What is Market Microstructure? My words:
Study of how trading actually occurs
Many economic and financial models assume that price is known
Price function of supply and demand
In reality, depends on information and strategy
Why you should care (as a quant)?
Microstructure affects transaction costs
Understanding microstructure can generate alpha or lower costs
Microstructure itself can be studied using quantitative techniques
Insert Presentation Title 10 September 2, 2012
11. Market Making Provide liquidity (immediacy) to the rest of the investing public
Always willing to buy or sell at certain prices
Difference is called the spread
Problem: information asymmetry with respect to the rest of the world
12. Questions about market making How should market makers set their quotes?
How/why do they (not) make (any) money?
13. An Economist’s View of Prices
14. Features of this Model Mathematically simple
Intuitively makes sense for most markets
Accurate way to view many markets
Increasing demand yields increasing price
Increasing supply yields declining price
… but it misses the key features about how prices are formed in financial markets
15. An Aside: Poker Simple one card poker, single suite deck
2 players each ante $1
Each player gets a card face down (they can see their own card)
Cards are ranked as normal
Game proceeds as follows:
16. One card poker game
17. Analysis of the Game If you could see the other persons card...
Strategy is trivial
Game is “fair”
But with hidden information...
Strategy is extremely nontrivial (the full game has been solved in this case but it’s hard)
The game is no longer fair.
“Bluffing” (concealing your private information) plays a role
See www.cs.cmu.edu/~ggordon/poker/ for more information
Thought question: who has the advantage?
18. What Assumptions Fail? Simple supply/demand curve analysis assumes everyone has perfect information
In reality, information is revealed through the trading process
Traders come to the marketplace with heterogenous information and sophistication, much like poker
19. Classic Microstructure Models Roll model: simplest model which incorporates market mechanics but no information/strategy
Sequential trade model (Glosten-Milgrom style): incorporates information asymmetry but no strategy
Kyle model: includes information asymmetry and strategy
Reference: Hasbrouck “Empirical Market Microstructure”
20. Roll Model for Prices Incorporates some notions that market mechanics and organization structure influence short term prices
Assumes fundamental security price follows a random walk
Trading occurs through dealer quotes
Spread is constant
Enables estimate of spread from trade prices
21. Roll Model Trade Prices Fair price m follows driftless random walk
Trades occur at dealer bid/offer quotes, spread is 2c
Each trade is independent and uninformative
22. Changes in trade price I
23. Changes in Trade Price II
24. Examples
25. Glosten-Milgrom Model Roll model is too simple
Captures some mechanical aspects of trading
Totally ignores information content
Sequential trade models include some aspects of information asymmetry
Glosten-Milgrom (1985) and many descendants
We refer to Hasbrouck (EMM as cited earlier) for a simplified version
26. Sequential Trading Setup Trading occurs at time t=0 in an asset with publicly unknown value: either V0 or V1 at time t=1.
Traders trade by placing market orders against marker maker quotations
B = bid
A = ask
Two types of traders:
I: informed. These traders know the true value and trade on that basis
U: uninformed. These traders (often called “noise” or “liquidity” traders) trade in a random direction
Dealers place quotes to compete p/l to 0.
Proportion of I to U is known to everyone.
27. STM: mechanics Security value is either V0 or V1 with probability d or 1-d respectively
Random trader arrives at market and is I or U with probability m or 1-m respectively
I traders trade in the direction of final value
U traders trade randomly
28. STM Mechanics
29. STM: How do dealers set quotations? As wide as possible...
Will not trade at an expected loss.
But because of competition, quotes will be competed down to expected P/L ~ 0
So, ask will be expected P/L realized from next trade conditioned on it being a BUY
This is a key point! Market makers should set their quotes at the expected terminal value conditioned on their quote getting hit
30. STM: analysis of ask P/L dealer gets from customer BUY: A-V
So, A=expectation of V conditioned on BUY
31. Observations Dealers always lose to informed and profit from uninformed.
Analysis of the bid is similar
32. Iterating the model This discussed a one period example
This can be iterated to handle sequences of trades as well
We assume each trader comes to the market only one time
Trade prices are reported publicly
Dealers all update their d on this basis
We don’t worry about inventory/risk concerns
33. Updating d The only state that changes over time is d
Computing new d after a first BUY order
34. Conclusions from model Trade prices form a martingale
Trades occur at bid/offer prices
These prices are expectation of terminal value conditioned on trade occurring at them
B then S cancel out
Order flow is not symmetric and is correlated over time (used to estimate probability of informed trading)
Eventually dealers have excellent estimate of terminal value
Prices gravitate towards one side or the other, spreads narrow
Trades have price impact
Important for empirical research
Measure of information asymmetry
35. Example
36. Thought question Regulatory proposal: solve the high frequency “problem” by imposing a minimum duration on limit orders
Q: What will the impact be of such a regulatory change?
A: It will increase the amount of information in the marketplace for others to trade against the limit order (for example, looking at futures prices)
In other words, the proportion of informed orders m increases
Hence, spreads widen
Insert Presentation Title 36 September 2, 2012
37. Roll model v. STM Roll model simply captures mechanics of dealer market with fixed edge per trade
STM gets at deeper notion of information in trade
Models reach incompatible conclusions
In Roll model, trade prices are mean reverting
In STM, trade prices are a Martingale
38. Strategic Trading In this sequential trade model, traders arrive at the market only once
They don’t need to worry about disguising their information from the dealers and other market participants
Dealers eventually learn the payoff (V0 or V1)
Strategic trade models address this shortcoming (bluffing in poker)
39. Kyle Model Liquidity traders net order flow u
One informed trader sees value v and submits x
Market maker observes y=u+x, sets price p
MM fills net order imbalance at price p
40. Analysis of Kyle Model Informed trader hypothesizes linear price response function from market maker
MM hypothesizes linear demand function from IT
Under normality assumption these turn out to be optimal
41. Single Period Analysis IT hypothesis:
P/L for IT
IT maximizes expected profit:
42. MM Strategy Hypothesis:
Solving:
Conclusion:
Knowing y, how to compute expectation of v? Apply bivariate conditional expectation to y and v
43. Discussion of IT Trading IT order flow function:
Trades in direction of terminal value
More uninformed flow leads to more trading
Less uncertainty on v leads to less trading
Expected P/L:
44. Market Maker Pricing Pricing function:
Perturbs p0 based on observed order flow
45. Iterated Auctions This can be repeated with MM updating distribution of v each round
Price is a Martingale: MM sets it as expectation of v conditioned on order flow observed up to that point
Informed trader slices orders into market over time, order flow tends to be on the same side (knowing IT’s order flow at any instant determines v).
However, total order flow has no autocorrelation:
Intuition: price changes and total order flow are linearly related, so price being a Martingale implies order flow is uncorrelated
46. Limitations Roll model hopelessly simplistic
Order flow and trades do reveal information
Ignoring this will lead to large losses
GM and Kyle models explain how information asymmetries influence the spread and MM P/L
But they take the information asymmetry as given, in reality the spread and trade prices/order flows are what can be observed.
Electronic markets prices are usually discrete
47. Needed: somthing in the middle
48. Adverse Selection Basic practical problem for MM is to combat adverse selection
Roll model too simplistic
Glosten-Milgrom and Kyle models focus on how AS arises from underlying (unobservable) information asymmetries
Desired: a model that focuses on the observable component of adverse selection
Main point: limit orders are always filled when you’re wrong, but only selectively when you’re right
Reasons for adverse selection
Informed incoming market orders
Competition among market makers
49. Simple AMM Model “Fair” price is 1 stage binary tree
Liquidate at time 1 at f.v.
Probability of price increase is p
Spread is 2s
We place a buy limit order
Probability of fill is q if price rises
Probability of fill is 1 if price falls
50. Compute the P/L
51. Simple Observations P/L increases with q. “Fill rate”
P/L increases with s. “spread”
P/L increases with p. “alpha” -- most of the time!
52. Why decreasing p? Q:How could we benefit from price falling when we’re buying?
A: Spread can more than compensate for alpha if large enough
Example: q=0, then only fills occur when price drops. P/L=(1-p)(s-1)
Decreasing p increases overall fill rate
53. Special Case: No Alpha No alpha, ie p=1/2
Breakeven occurs when fill rate q is sufficiently high
54. Special Case: s=1/2 s=1/2
This looks like many limit order books if f.v. is assumed to be the midquote
In words, no liquidity rebate or fee
55. Lessons from the Model P/L of automated market making is a tradeoff between three quantities
Spread: s (obvious)
Alpha: p (somewhat obvious)
Fill rate: q (subtle but perhaps most important)
Math that goes into maximizing these
p: predictive models of price (regression, machine learning, etc)
q: modeling fills rates, queues, etc
56. Break Even Spread
57. Multi-period Extensions So far a single period model dictates when it makes sense to post a limit order or not
String these together to get a multi-period model
Forecasts should not be viewed as static: p has some dynamics
Interesting to see what happens when q also varries dynamically
58. AMM Model Dynamics Price is a binary process with transition probabilities that vary stochastically as function of state variable p
p itself is binary process. Transition probabilities are a function of p itself, mean reverting
Probability of adverse fill is modeled similarly to p
59. AMM Model Dynamics
60. Apply HJB Equations above give 3d state space (p, q and position s)
Assume terminal time T with specified quadratic value function V(T,s,p,q) = -k s2
Use HJB to go backwards in time to fill in value function for t<T
61. Numerical Examples
62. Conclusions…